What is the limit as x approaches infinity of x(x+1) ?

The limit as x approaches infinity of x(x+1) is infinity

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limit as x approaches infinity of x(x+1)

x \to \infty lim (x (x + 1))

\infty

Solution steps

x \to \infty lim (x (x + 1))

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

With the exception of indeterminate form

= x \to \infty lim (x) \cdot x \to \infty lim (x + 1)

x \to \infty lim (x) = \infty

x \to \infty lim (x + 1) = \infty

= \infty \cdot \infty

Apply Infinity Property:

\infty \infty = \infty

= \infty

d er i v a t i v e f (x) = \frac{x}{x ^{2} + 2}

x \to 6 lim (\frac{1}{x} - \frac{1}{6})

f (t) = - 3 sin (t)

d er i v a t i v e 3 \cdot 4^{x}

\frac{d}{d x} (cos^{2} (4 x))

What is the limit as x approaches infinity of x(x+1) ?
The limit as x approaches infinity of x(x+1) is infinity